Answers

First, it's not really relevant to your question, but you are missing an opening <tr> at the beginning of your form and a closing </tr> at the end of your form. I've added them in below.

This is untested, but the gist of it is that you create two hidden form fields, one for each age value. Then, in the slide handler of the slider, you set the value of those inputs to be the value of the corresponding slider. In your PHP code, you'll use $_POST['age_from'] and $_POST['age_to'].

The code you provide doesn't give the whole form (assuming that you are using a form), but the way you have it you just need to add name attribute to the input, example name="age_from" and once posted you will be able to capture the value with $_POST['age_from']